Turkey's President Recep Tayyip Erdogan attends a wreath-laying ceremony at the Ninos Heroes monument at Chapultepec Park in Mexico City February 12, 2015. REUTERS/Edgard Garrido

MEXICO CITY (Reuters) - Turkish President Tayyip Erdogan on Thursday criticized U.S. President Barack Obama for his silence following the killings of three young Muslims in North Carolina this week, in the latest sign relations between the two leaders have become strained.

Speaking alongside Mexican President Enrique Pena Nieto during a state visit to Latin America’s No. 2 economy, Erdogan said the silence of Obama, Vice President Joe Biden and Secretary of State John Kerry was “telling” and they should take a position following such acts.

“If you stay silent when faced with an incident like this, and don’t make a statement, the world will stay silent towards you,” Erdogan said, condemning those responsible for the crime.

The three Muslims were shot dead on Tuesday near the University of North Carolina campus in an incident police said was possibly a hate crime. The White House said on Wednesday it would await the results of the police investigation before commenting.

Newlywed Deah Barakat, 23, a University of North Carolina dental student, his wife Yusor Abu-Salha, 21, and her sister, Razan Abu-Salha, 19, a student at North Carolina State University, were gunned down on Tuesday in a condominium about two miles (three km) from the UNC campus in Chapel Hill.

Police charged the couple’s neighbour, Craig Stephen Hicks, 46, with murder. Investigators say initial findings indicate a dispute over parking prompted the shooting but they are looking into whether Hicks was motivated by hatred towards the victims because they were Muslim.

Turkey, a European Union candidate nation and member of the NATO military alliance, is a key U.S. ally in the fight against Islamic jihadists. But Erdogan, a devout Sunni Muslim, has become increasingly outspoken about what he sees as rising Islamophobia in the West.

Last year, Erdogan said his relations with Obama had become strained and that he no longer spoke directly with him as he was disappointed by a lack of U.S. action over the war in neighbouring Syria. Erdogan said he instead spoke with Biden over issues such as Iraq.

Despite working together to combat the Islamic State, differences have arisen between the United States and Turkey over how best to tackle the insurgents.

Turkey has been an opponent of Syrian President Bashar al-Assad, backing rebels fighting to oust him and allowing the political opposition to organise on Turkish soil. It long lobbied for international intervention in the war.

Reporting by Alberto Fajardo; Writing by Gabriel Stargardter and Christine Murray; Editing by James Dalgleish